Significant figures and

In this experiment students measure the length of a pestle using a wooden meter stick, a stainless-steel ruler, and a vernier caliper. The data collected in this experiment provide an opportunity to discuss significant figures and sources of error. Statistical analysis includes the Q-test, f-test, and F-test. 

Note To find e-95 66, take the inverse In of-95.66 on your calculator, inv In of-95.66 = 2.85 x 10 42. Keep one more significant figure and round off to three significant figures at the end, particularly when working with logarithms. 

Note Keep all the significant figures and round at the end. Remember the number of decimal places in pH or pOH values are set by the number of significant figures in the [H+] or [OH-] this is a result of working with logarithms. 

B Unfortunately, we cannot use the result of Example 26-5 ( 0.0045 u = 4.2 MeV ) because it is expressed to only two significant figures, and we begin with four significant figures. But, we essentially work backwards through that calculation. The last conversion factor is from Table 2-1. 

Tables E14.3C and E14.3D list values of the variables at x (rounded to five significant figures) and the constraints, respectively, at the optimal solution.

The measurement system that is most widely used in chemistry is the SI system. It incorporates a base unit for the various quantities and then uses prefixes to moderate the value of the base unit. The Unit Conversion Method is a way to generate easily the setup to a problem. Be sure to round off the final answer to the correct number of significant figures and include the units with the final answer. 

This calculation leaves us with the appropriate number of significant figures and the correct units. 

We need to appreciate from the above calculation that a huge difference in activity is represented by a very small difference between E and in part because of the square term in the Nemst-equation denominator. This explains why it is essential to have a good quality voltmeter (i.e. one having a nearinfinite resistance R and with the ability to display the emf to several significant figures) and to take readings only when true equilibrium has been reached. 

One or more final zeros (zeros that end the measurement) used after the decimal point are significant. So 1.760 has four significant figures, and 1.7600 has five significant figures. The number 0.0001200 has only four significant figures because the first zeros are not final. 

The discrepancy between the two values of a is a matter of significant figures and is not meaningful. ... 

Final zeros after the decimal point are significant figures and are used to indicate the decimal place to which the measurements are reliable. Thus 1.0 cm indicates a length reliably known to tenths of a centimeter but not to hundredths of a centimeter, whereas 1.000 cm indicates a length reliably known to thousandths of a centimeter. A very common mistake is leaving out these zeros when the measured quantity has an integral value. 

Suppose that the recorded length of an object is 15.7 cm. By convention, this means that the length was measured to the nearest 0.1 cm and that its exact value lies between 15.65 and 15.75 cm. If this measurement were exact to the nearest 0.01 cm, it would have been recorded as 15.70 cm. We say that the first measurement is accurate to 3 significant figures and the second to 4. 

For example, a concentration 100.9 mg/1 expressed in four significant figures indicates that only the fourth digit (9) has some uncertainty. If the same result is rounded off to three significant figures and becomes 101 mg/1, the last digit of the three (1) has uncertainty associated with it. 

In nearly all practical chemical calculations, a precision of only two to four significant figures is required. Therefore the student need not perform multiplications and divisions manually. Even if an electronic calculator is not available, an inexpensive 10-in slide rule is accurate to three significant figures, and a table of 4-place logarithms is accurate to four significant figures. 

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